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UID:8992@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20260210T110000
DTEND;TZID=Europe/Paris:20260210T120000
DTSTAMP:20260202T074802Z
URL:https://www.i2m.univ-amu.fr/evenements/seminaire-ernest-4/
SUMMARY:Alonso Herrera Nuñez (LIX): On the topological structure of the sp
 ace of ℤᵈ-subshifts
DESCRIPTION:Alonso Herrera Nuñez: The space 𝓢ᵈ of ℤᵈ-subshifts\, 
 d≥1\, endowed with the Hausdorff topology\, provides a natural framework
  for the study of generic properties\, as it admits an interpretation in t
 erms of languages. For one-dimensional systems several generic properties 
 have been characterised and\, in a recent work\, Pavlov and Schmieding hav
 e finished painting the picture: they characterised isolated points and sh
 owed that they completely account for generic systems and the non-perfect 
 structure of 𝓢¹\, as the Cantor-Bendixson rank of the space is 1. For 
 higher-dimensional systems the picture has yet to be finished.\n\nIn this 
 talk\, we revisit a previous joint work with Silvère Gangloff\, where we 
 characterised isolated points in 𝓢ᵈ in terms of maximal subsystems 
 –this characterisation allows\, in particular\, to recover the one-dimen
 sional characterisation. We discuss the existence of a non-isolated subshi
 ft that can only be approximated by isolated systems\, making it isolated 
 in the derived set of 𝓢ᵈ\, and then iterate this construction to prod
 uce analogous systems at every finite level of the Cantor-Bendixson proces
 s\, showing that the Cantor-Bendixson rank of 𝓢² is infinite. Finally\
 , we present our latest progress on this topic: we propose a complementary
  approach based on the lattice of subsystems and its order-theoretic struc
 ture. This new perspective allows us to shed light on the structure of iso
 lated points in the derivative of 𝓢ᵈ.\n\njoint with Silvère Gangloff
CATEGORIES:Séminaire,Ernest
LOCATION:I2M Luminy - TPR2\, Salle de Séminaire 304-306 (3ème étage)\, 1
 63 Avenue de Luminy\, Marseille\, 13009\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=163 Avenue de Luminy\, Mars
 eille\, 13009\, France;X-APPLE-RADIUS=100;X-TITLE=I2M Luminy - TPR2\, Sall
 e de Séminaire 304-306 (3ème étage):geo:0,0
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